Currently, the most reliable rockets are maybe 99% reliable but certainly not 99.9%. If you are trying to send nuclear material to space, you have to account for the possibility that

* The rocket blows up on the launchpad

* The rocket gets you part way up, then blows up during ascent

* The rocket fails before orbital insertion, and your nuclear payload re-enters the atmosphere at near-orbital velocity

In all of those cases, you need to have enough shielding to avoid spreading nuclear waste over a very large area -- that adds a lot of mass. And everyone whose jurisdiction you're launching over needs to trust you have enough shielding. And in the case where it fails during orbit insertion and re-enters the atmosphere, you don't have a lot of control on where the nuclear materials end up, which has proliferation issues.

> In all of those cases, you need to have enough shielding to avoid spreading nuclear waste over a very large area -- that adds a lot of mass.

Conservatively it might add an order of magnitude, and likely less. This still renders future reusable launchers much cheaper per kg of spent fuel than reprocessing would be, unless you are projecting very large improvements in the cost of reprocessing.

You might object current launchers aren't cheap enough, but I wasn't proposing doing this right now with current launchers, so that would be a strawman objection.